Data-driven fuzzy analysis in quantitative mineral resource assessment

The integration of geo-information from multiple sources and of diverse nature in developing mineral favourability indexes (MFIs) is a well-known problem in mineral exploration and mineral resource assessment. Fuzzy set theory provides a convenient framework to combine and analyse qualitative and quantitative data independently of their source or characteristics. A novel, data-driven formulation for calculating MFIs based on fuzzy analysis is developed in this paper. Different geo-variables are considered fuzzy sets and their appropriate membership functions are defined and modelled. A new weighted average-type aggregation operator is then introduced to generate a new fuzzy set representing mineral favourability. The membership grades of the new fuzzy set are considered as the MFI. The weights for the aggregation operation combine the individual membership functions of the geo-variables, and are derived using information from training areas and L, regression. The technique is demonstrated in a case study of skarn tin deposits and is used to integrate geological, geochemical and magnetic data. The study area covers a total of 22.5 km(2) and is divided into 349 cells, which include nine control cells. Nine geo-variables are considered in this study. Depending on the nature of the various geo-variables, four different types of membership functions are used to model the fuzzy membership of the geo-variables involved. (C) 2002 Elsevier Science Ltd. All rights reserved.

Off-line signature verification and forgery detection using fuzzy modeling

Automatic signature verification is a well-established and an active area of research with numerous applications such as bank check verification, ATM access, etc. This paper proposes a novel approach to the problem of automatic off-line signature verification and forgery detection. The proposed approach is based on fuzzy modeling that employs the Takagi-Sugeno (TS) model. Signature verification and forgery detection are carried out using angle features extracted from box approach. Each feature corresponds to a fuzzy set. The features are fuzzified by an exponential membership function involved in the TS model, which is modified to include structural parameters. The structural parameters are devised to take account of possible variations due to handwriting styles and to reflect moods. The membership functions constitute weights in the TS model. The optimization of the output of the TS model with respect to the structural parameters yields the solution for the parameters. We have also derived two TS models by considering a rule for each input feature in the first formulation (Multiple rules) and by considering a single rule for all input features in the second formulation. In this work, we have found that TS model with multiple rules is better than TS model with single rule for detecting three types of forgeries; random, skilled and unskilled from a large database of sample signatures in addition to verifying genuine signatures. We have also devised three approaches, viz., an innovative approach and two intuitive approaches using the TS model with multiple rules for improved performance. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.